Populations of excited atoms that all have the same z component of velocity can be produced by pumping a vapor with a narrow-band laser. This velocity-selected population is then thermalized by velocity-changing collisions. However, in a pure vapor, even at low densities where velocity-changing collisions can be ignored, the mechanisms of radiation trapping and resonance exchange collisions can still lead to substantial thermalization of excited-atom velocity distributions. In this paper, we present data demonstrating these effects. We compare our data with results from a simple model of these processes. The model is in qualitative agreement with the experimental results.